Electromechanical properties of ferroelectric thin films have drawn a lot of attention because of their applications in sensors, actuators and microelecrtromechanical devices. Their electrical properties not only depend on the electrical loading but also on the mechanical one. Similarly, the mechanical properties are influenced by both electrical and mechanical loadings. The coupling between the electrical and mechanical effects is obviously important for these phenomena. Thus, it is worthwhile to investigate these properties in order to understand the switching mechanisms behind the various phenomena and to optimize the device performance. In this project, these properties were investigated theoretically using a modified two-dimensional four-state Potts model. It has been established that 90° domain-wall switching is responsible for electromechanical properties. Consequently, any theory that intends to explain or simulate electromechanical properties in microscopic scale should have the description and formulation to tackle this 90° domain-wall switching. Four-state Potts model provides a simple picture to meet this requirement. In my present work, the ferroelectric thin film is modelled by a two-dimensional array of dipoles and each of which is represented by a pseudo-spin. There are four possible states for the pseudo-spin which are mutually perpendicular to each other. The dipole orientation is associated with the deformation of a perovskite cell, through the ferroelastic effect. Consequently, there are also two strain states, correlated with the pseudo-spin states according to the dipole orientation. In addition to the coupling of neighbouring dipoles and that between the dipoles and the electric field as in the Hamiltonian of a conventional Potts model or Ising model, the mechanical energy density and the coupling between neighbouring strain states are also incorporated in the Hamiltonian of our model. Moreover, the effect of anisotropic switching is also taken into account. The evolution of the ensemble of pseudo-spins and strain states can then be determined using the conventional metropolis algorithm. The macroscopic properties, such as polarization and strain, are then evaluated from the ensemble of pseudo-spins and strain states.Stress always exists in ferroelectric films. The presence of stress alters the ferroelectric properties of thin films, such as phase transition temperature, polarization and strain. Experimental accounts on the effects of stress are numerous [Garino and Harrington, 1992; Kushida and Takeuchi, 1990; Kushida and Takeuchi, 1991; Rossetti et al., 1991; Shepard et al., 1996; Taylor et al., 2002; Yuzyuk et al., 2002]. For instance, the paraelectric-ferroelectric phase transition temperature can be determined from either the polarization versus temperature or susceptibility versus temperature relations. Only the electric field perpendicular to the film surface was applied to the system throughout our work. The shift in phase transition temperature in the presence of stress was obtained and compared with experimental results qualitatively [Abe and Komatsu, 1995; Taylor et al., 2002; Yuzyuk et al., 2002]. Moreover, we have also simulated the polarization-electric field and electric displacement-electric field hysteresis loops as well as the strain-electric field butterfly loops under different loading conditions: (i) static stress with alternating electric field and (ii) alternating stress and electric field. For the former one, as observed from experiments, the presence of either in-plane tensile stress or longitudinal compressive stress reduces both the remnant and saturated polarizations. On the other hand, either in-plane compressive stress or longitudinal tensile stress leads to opposite effect. The corresponding strain responses of the thin films were also obtained. In particular, the dynamic change in strain over a cycle was enhanced under the following conditions: (i) in-plane tensile stress, (ii) uni-axial compressive stress, and (iii) small anisotropic switching factor øc. The experimental result on the dielectric and strain responses under combined electrical and mechanical loadings investigated by Zhou and Kemlah [Zhou and Kamlah, 2004] was also numerically simulated. It was found that when the alternating electric field and the uni-axial compressive stress are in phase, the dynamic changes for both electric displacement and strain are reduced. On a contrary, they are enhanced when both loadings are out-of-phase. Explanation to this novel behavior is presented in this thesis.

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